2. Let X1 and X2 be sets. Define functions T1 : X1 × X2 → X1, T2 : X1 × X2 → X2 by T| (X1, X2) = x1, T2(x1, x2) = x2 (x1 E X1, x2 e X2). Also let A be a set, and let fi : A → X1, f2 : A → X2 be functions. Prove that there is exactly one function f : A → X1 × X2 such that 1 • f = fi and t2 • f = f2.

2. Let X1 and X2 be sets. Define functions T1 : X1 × X2 → X1, T2 : X1 × X2 → X2 by T| (X1, X2) = x1, T2(x1, x2) = x2 (x1 E X1, x2 e X2). Also let A be a set, and let fi : A → X1, f2 : A → X2 be functions. Prove that there is exactly one function f : A → X1 × X2 such that 1 • f = fi and t2 • f = f2.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 25E: 25. Let, where and are non empty, and let and be subsets of . Prove that. Prove that. Prove...

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